Tuesday, May 16, 2023, 2pm
Elena Di Bernardino (Université Côte d’Azur, Nice)
Geometry of random excursion sets
The excursion sets of a smooth random field carries relevant information
in its various geometric measures. After an introduction of these
geometrical quantities showing how they are related to the parameters of the field, we focus on the problem of discretization. From a computational
viewpoint, one never has access to the continuous observation of the excursion set, but rather to observations at discrete points in space. It has been reported that for specific regular lattices of points in dimensions 2 and 3, the usual estimate of the surface area of the excursions remains biased even when the lattice becomes dense in the domain of observation.
We show that this limiting bias is invariant to the locations of the
observation points and that it only depends on the ambiant dimension
(based on joint works with H. Biermé, R. Cotsakis, C. Duval and A.